The Order of Real Numbers: Inequalities

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  • 0:07 Which Is Bigger?
  • 0:32 Less Than or Greater Than
  • 1:15 How to Use Inequalities
  • 4:03 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

An inequality is an operation describing how one number can be compared to another. This lesson will describe and define inequalities and the symbols used to represent them. It will also give some examples on how to work with inequalities.

Which is Bigger?

When you were little, did your teacher ever ask your class to line up from tallest to smallest? Or have you ever lined something from smallest to greatest? I know I like the spice jars in the cabinet in my house to be lined up according to size. This type of organization deals with deciding the 'unequalness' of things, which of them are bigger or which of them are smaller than all the others.

Less Than or Greater Than

In mathematics, lining up numbers according to size involves the use of inequalities. An inequality is the relationship between two values that are different. Working with inequalities involves determining what that relationship is -- how each number is bigger or smaller than the other numbers in a particular group. The notation for inequalities consists of the following symbols:

Inequality symbols
inequality symbols

These symbols are used to notate exactly what they say. If you have two quantities, the symbols can be used to show which one is larger or smaller than the other.

How to Use Inequalities

Inequalities can be used in many different ways. First, they can be used to show the relationship between two quantities. For example:

1 < 13


7.5 > 7.2

Inequalities are a good way to show the differences between real numbers that might not be easily apparent at a glance.

Real numbers are all numbers that are not imaginary. They include the following sets of numbers:

  • Whole numbers, which are non-negative numbers that are not fractions or decimals.
  • Integers , which are all numbers that are not fractions or decimals, including negative numbers.
  • Rational numbers are positive and negative numbers that include fractions and decimals.
  • Irrational numbers include decimal numbers that cannot be written as fractions, for example: e and pi.

Here's another example:

sqrt. 2 < pi

2/3 > 0.15

The second way you can use inequalities is to solve problems, such as:

Given the inequality a < b, write another inequality with the same meaning.

Answers to this question might be things like:

2 < 6


1.8 > sqrt. 3

Lastly, inequalities can be used to write true or false statements, such as:

Is the statement '-5 is greater than or equal to -3' true or false?

For problems like these, if it's not easy to see the answer, it can be helpful to draw a number line to help you figure it out.

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